Example Algorithm for Steps in Solving Closed-Ended Problems

1. Statement

   The elementary, liquid-phase, irreversible reaction

   

   is to be carried out in a flow reactor. Two reactors are available, an 800 dm³ PFR that can only be operated at 300 K and a 200 dm³ CSTR that can be operated at 350 K. The two feed streams to the reactor mix to form a single fee d stream that is equal molar in A and B, with a total volumetric flowrate of 10 dm³/min. Which of the two reactors will give us the highest conversion?

   Additional Information:

   at 300 K, k = 0.07 dm3/mol-min E = 85000 J/mol-K CA0B = CB0B = 2 mol/dm 3 vA0 = vB0 = 0.5*v0 = 5 dm3/min

2. Real Problem

   We have two choices, a PFR operated at 300 K and a CSTR operated at 350 K. Which one do we choose?

   
   

3. Sketch

   

   

   
   
4. Identify and Name
   1. Relevant Theories and Equations

      Arrhenius Equation:
      The higher the temperature, the faster the reaction rate.

      
      

      Rate Law:

      Mole Balances:

   2. Systems

      Volume of CSTR
      Volume of PFR

   3. Dependent and Independent Variables

      Independent: V, F_A0, T
      Dependent: X

   4. Knowns and Unknowns

      Knowns: k₀, E, V, n₀, C_A0B, C_B0B
      Unknowns: X

   5. Inputs and Outputs

      In: F_A0 = F_B0, so Q_B = 1
      Out: F_A = F_A0(1-X), F_B = F_A0(1-X), F_C = F_A0X

   6. What color should we paint the reactor?

      Not an issue.

   
   

5. Assumptions

   Isothermal, no pressure drop. The CSTR is well mixed. There are no radial variations in the PFR.

   
   

6. Specifications

   There is neither too much redundant information, nor is there too little information given. Therefore, the problem is neither over-specified, nor under-specified.

   
   

7. Similar or Related Example Problems

   This problem has a solution procedure in common with Examples 4-2 and 4-4 in the text.

   
   

8. Algorithm

   CSTR

   PFR

   
   
   1. Mole Balance

   2. Rate Law

      

   3. Stoichiometry - liquid, v = v_o; equal molar \ Q_B = 1

      

      C_A = C_A0(1-X)

      C_B = C_A0(1-X)

   4. Combine
      
      (eqn 1)

      
      (eqn 2)

   5. Evaluate
            v _A0 = 5 dm³/min
      Before mixing
            C_A0B = 2 mol/dm³
            F_A0 = C_A0B* v_A0
            F_A0 = (5 dm³/min)(2 mol/dm³) = 10 mol/min
      After mixing
            v₀ = v_A0 + v_B0 = 5 dm³/min + 5 dm³/min = 10 dm³/min
           C_A0 = 1 mol/dm³
           

      	at 350 K,
      		k = 8.447 dm3/mol-min

9. Manipulate
   1. CSTR @ 350 K

      the combined CSTR equation (eqn 1) can be arranged as
      
      
      
      
      
      

   2. PFR @ 300 K

      
      
      

   Choose the CSTR, because it gives the highest conversion.

   
   

10. Units Check

    X is dimensionless

    
    

11. Is it reasonable?

    This is a reasonable conversion.

This the end of the PFR/CSTR example. A sample registration exam problem is also available.

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